A350931
Maximal determinant of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 7, 105, 2294, 71753, 3051554, 175457984
Offset: 0
a(2) = 7:
[3 1]
[2 3]
a(3) = 105:
[5 1 3]
[4 5 1]
[2 4 5]
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from itertools import permutations
from sympy import Matrix
def A350931(n): return max(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A350937
Minimal permanent of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 7, 89, 2287, 89025, 5141775, 404316249
Offset: 0
a(2) = 7:
1 2
3 1
a(3) = 89:
1 2 4
3 1 2
5 3 1
-
from itertools import permutations
from sympy import Matrix
def A350937(n): return 1 if n == 0 else min(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).per() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A350953
Minimal determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.
Original entry on oeis.org
1, 1, -3, -12, -100, -1749, -47600, -800681, -39453535, -1351201968, -66984136299, -2938096403400, -235011452211680
Offset: 0
a(3) = -12:
2 3 1
3 2 3
1 3 2
a(4) = -100:
3 4 1 2
4 3 4 1
1 4 3 4
2 1 4 3
a(5) = -1749:
5 4 1 3 2
4 5 4 1 3
1 4 5 4 1
3 1 4 5 4
2 3 1 4 5
-
from itertools import permutations
from sympy import Matrix
def A350953(n): return min(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).det() for p in permutations(range(1,n+1))) # Chai Wah Wu, Jan 27 2022
A350932
Minimal determinant of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers, with a(0) = 1.
Original entry on oeis.org
1, 2, -11, -286, -57935, -5696488, -1764195984, -521528189252
Offset: 0
a(2) = -11:
2 3
5 2
a(3) = -286:
5 7 2
11 5 7
3 11 5
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f:= proc(n) local i;
min(map(t -> LinearAlgebra:-Determinant(LinearAlgebra:-ToeplitzMatrix(t)), combinat:-permute([seq(ithprime(i),i=1..2*n-1)]))) end proc:
f(0):= 1:
map(f, [$0..5]); # Robert Israel, Apr 01 2024
-
from itertools import permutations
from sympy import Matrix, prime
def A350932(n): return min(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(prime(i) for i in range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A358567
a(n) is the minimal determinant of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).
Original entry on oeis.org
1, 0, -2, -31, -1297, -39837, -2256911, -99518694
Offset: 0
a(2) = -2:
[0, 1;
2, 0]
a(3) = -31:
[2, 3, 0;
4, 2, 3;
1, 4, 2]
Showing 1-5 of 5 results.
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